### Abstract

We test the Franck-Condon (FC) approximation for chemical reactions by prescribing a simple construction of quasiadiabatic potential energy surfaces and evaluating numerically FC overlap integrals for the collinear case of the chemical reactions H_{2}(D_{2}) + F and H + Cl_{2}. The FC model is derivable from the exact transition matrix by the use of four basic approximations: neglect of virtual transitions to excited electronic states; Born-Oppenheimer approximation; neglect of nuclear-electronic couplings; and the Franck-Condon approximation. The wave functions involved in the FC overlap are determined from quasiadiabatic potential surfaces, which were chosen to be constructed from the corresponding LEPS and anti-LEPS adiabatic surfaces for the chemical reaction in question. A coupling function which involves a single free parameter is needed to connect the quasiadiabatic surfaces. Our calculations show that the results are insensitive to this free parameter. We calculate vibrational distributions of reaction products for various initial kinetic energies of reactants and find the results to be in good qualitative agreement with both exact quantal calculations and FC models which include further approximations (with compensatory ease of calculation). Our results agree with the maximum in the vibrational distribution predicted by the other calculations and show similar trends with variation in initial relative kinetic energy and the masses (including isotopic substitution) as well as certain features of the potential surface.

Original language | English |
---|---|

Pages (from-to) | 2414-2424 |

Number of pages | 11 |

Journal | Journal of Chemical Physics |

Volume | 70 |

Issue number | 5 |

Publication status | Published - 1979 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Journal of Chemical Physics*,

*70*(5), 2414-2424.

**Franck-Condon factors in studies of dynamics of chemical reactions. V. Simple construction of quasiadiabatic potential energy surfaces and numerical evaluation of Franck-Condon integrals.** / Vilá, Carlos L.; Kinsey, James L.; Ross, John; Schatz, George C.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 70, no. 5, pp. 2414-2424.

}

TY - JOUR

T1 - Franck-Condon factors in studies of dynamics of chemical reactions. V. Simple construction of quasiadiabatic potential energy surfaces and numerical evaluation of Franck-Condon integrals

AU - Vilá, Carlos L.

AU - Kinsey, James L.

AU - Ross, John

AU - Schatz, George C

PY - 1979

Y1 - 1979

N2 - We test the Franck-Condon (FC) approximation for chemical reactions by prescribing a simple construction of quasiadiabatic potential energy surfaces and evaluating numerically FC overlap integrals for the collinear case of the chemical reactions H2(D2) + F and H + Cl2. The FC model is derivable from the exact transition matrix by the use of four basic approximations: neglect of virtual transitions to excited electronic states; Born-Oppenheimer approximation; neglect of nuclear-electronic couplings; and the Franck-Condon approximation. The wave functions involved in the FC overlap are determined from quasiadiabatic potential surfaces, which were chosen to be constructed from the corresponding LEPS and anti-LEPS adiabatic surfaces for the chemical reaction in question. A coupling function which involves a single free parameter is needed to connect the quasiadiabatic surfaces. Our calculations show that the results are insensitive to this free parameter. We calculate vibrational distributions of reaction products for various initial kinetic energies of reactants and find the results to be in good qualitative agreement with both exact quantal calculations and FC models which include further approximations (with compensatory ease of calculation). Our results agree with the maximum in the vibrational distribution predicted by the other calculations and show similar trends with variation in initial relative kinetic energy and the masses (including isotopic substitution) as well as certain features of the potential surface.

AB - We test the Franck-Condon (FC) approximation for chemical reactions by prescribing a simple construction of quasiadiabatic potential energy surfaces and evaluating numerically FC overlap integrals for the collinear case of the chemical reactions H2(D2) + F and H + Cl2. The FC model is derivable from the exact transition matrix by the use of four basic approximations: neglect of virtual transitions to excited electronic states; Born-Oppenheimer approximation; neglect of nuclear-electronic couplings; and the Franck-Condon approximation. The wave functions involved in the FC overlap are determined from quasiadiabatic potential surfaces, which were chosen to be constructed from the corresponding LEPS and anti-LEPS adiabatic surfaces for the chemical reaction in question. A coupling function which involves a single free parameter is needed to connect the quasiadiabatic surfaces. Our calculations show that the results are insensitive to this free parameter. We calculate vibrational distributions of reaction products for various initial kinetic energies of reactants and find the results to be in good qualitative agreement with both exact quantal calculations and FC models which include further approximations (with compensatory ease of calculation). Our results agree with the maximum in the vibrational distribution predicted by the other calculations and show similar trends with variation in initial relative kinetic energy and the masses (including isotopic substitution) as well as certain features of the potential surface.

UR - http://www.scopus.com/inward/record.url?scp=0001130248&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001130248&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0001130248

VL - 70

SP - 2414

EP - 2424

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 5

ER -